Question

Which function represents the same relationship?

Answer 1

Answer:

B

Step-by-step explanation:

We can use the standard form of an exponential function:

$y=a(b)^x$

The point (0, 18) tells us that y = 18 when x = 0. Hence:

$\displaystyle 18=a(b)^0$

Simplify:

$a=18$

Our equation is now:

$\displaystyle y=18(b)^x$

Next, the point (-1, 15) tells us that y = 15 when x = -1. Hence:

$15=18(b)^{-1}$

Isolate the variable:

$\displaystyle \frac{1}{b}=\frac{5}{6}$

Hence:

$\displaystyle b=\frac{6}{5}$

By substitution:

$\displaystyle y=18\left(\frac{6}{5}\right)^x$

Our answer is B.